curve #3037

y² + xy = x³ − 521898581151662383158650415466x + 139102677048540476550558210975450499388872100

a-invariants: [1, 0, 0, -521898581151662383158650415466, 139102677048540476550558210975450499388872100]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 2958865796524431023234757779070
discriminant (Δ): 738832923014727520277890809204373654417532918601880336543868106634446233686024282271846400
Faltings height: 16.0050
naive height: 216.8954
primes of bad reduction: 2, 3, 5, 11, 17, 19, 23, 29, 37, 41, 43, 53, 59, 71, 73, 12569, 3131981
regulator: 47041091.6224858328000843278835972875149535894312386238
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:21 UTC
last updated: 2026-09-26 20:34:21 UTC

Witness: 8 independent points log in to add more points →

(329822230580036, 1687565207858244545030)
(339674215029686, 1009114376200243682234)
(302154232422500, 2999106591792166425110)
(-199734351443992, -15341955029071957267834)
(29871458072000, 11114830612904501597990)
(-580988662510316, -15691028220629492394074)
(340328699602681364, 198539481505542503412693830)
(97457855700918346/49, 28633912063299364148293828/343)

Commentary

Dujella - Peral - Tadic (2019). Source: https://dujella.github.io/tors/z6old678.html (curve entry 30). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:34:21 UTC · history